Seminar: Conder / Sarnak -- Symmetry and Chirality in Discrete Structures / Zeroes and Nodal Lines of Modular Forms

Next Friday 26 August we have a fabulous double-header of talks with Marston Conder
(University of Auckland) giving a colloquium at 12 PM (the usual algebra seminar slot)
on Symmetry and Chirality in Discrete Structures and Peter Sarnak (Princeton
University/IAS) presenting his Mahler lecture at 2:30 PM on Zeroes and Nodal Lines of
Modular Forms.  All are welcome to join for the lunch in between these talks at 1 PM at
the Forum restaurant.  



On Thursday 25 August Peter Sarnak will give a public lecture at the University of New
South Wales, 3:30 PM on Chaos, Quantum Mechanics and Number Theory.  



Information on the Mahler Lectures and details of the three talks are below.  



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The Mahler Lectures are a biennial activity organised by the Australian Mathematical
Society with the assistance of the Australian Mathematical Sciences Institute.  

Initiated by a bequest from number theorist Kurt Mahler, it brings a renowned
mathematician to Australia to give a lecture tour (including public lectures) of
Australian universities.  



This year’s Mahler lecturer is Peter Sarnak, Eugene Higgins Professor of Mathematics at
Princeton University and Professor at the the Institute for Advanced Study in
Princeton.  He is a legendary figure in modern number theory.  Peter Sarnak will be in
Australia from August 8 till August 27 and will give 13 lectures at 9 different
universities in 6 different cities.  



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Speaker: Marston Conder, University of Auckland 



Date: Friday 26 August, 12:05-12:55pm 



Location: Carslaw 175 



Title: Symmetry and chirality in discrete structures 



Abstract: 



Symmetry is pervasive in both nature and human culture.  The notion of chirality (or
‘handedness’) is similarly pervasive, but less well understood.  



In this lecture I will talk about a number of situations involving discrete objects that
have maximum possible symmetry in their class, or maximum possible rotational symmetry
while being chiral.  



Examples include graphs (networks), maps (graphs embedded on surfaces), compact Riemann
surfaces (equivalence to algebraic curves), and polytopes (abstract geometric
structures).  



In such cases, maximum symmetry can often be modelled by the action of some universal
group, the non-degenerate quotients of which are the symmetry groups of individual
examples.  The use of computational systems (like MAGMA) can be very helpful in
producing examples, and then revealing patterns among them, or providing answers to
various questions.  



An intriguing question in some of these situations is about the prevalence of chirality:
among small examples, how many are reflexible and how many are chiral? and what happens
asymptotically? 



...........................................................................  

 1 PM: Lunch at the Forum Restaurant, Darlington Centre.  All welcome.
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Friday, Aug.  26, Sydney University, 2.30pm, Room 175, Carslaw Building, Colloquium 



Zeroes and Nodal Lines of Modular Forms 



One of the consequences of the recent proof by Holowinski and Soundararajan of the
holomorphic "Quantum Unique Ergodicity Conjecture" is that the zeros of a classical
holomorphic hecke cusp forms become equidistributed as the weight of the form goes to
infinity.  We review this as well as some finer features (first discovered numerically)
concerning the locations of the zeros as well as of the nodal lines of the analogous
Maass forms.  The latter behave like ovals of random real projective plane curves, a
topic of independent interest.  



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